right triangle trigonometry - mr. velazquez's class website · right triangles and...
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Right Triangle Trigonometry
Honors Precalculus
Mr. Velazquez
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Right Triangles and Trigonometry
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Right Triangles and Trigonometry
Trig values for a given angle are always the same, no matter how large the triangle is, due to the Law of Similar Triangles.
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Right Triangles and Trigonometry
Find the value of each of the six trigonometric functions for 𝜃 if 𝑏 = 4 and 𝑐 = 2 5.
4b
2 5c
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Right Triangles and Trigonometry
Find the value of 𝑏 and 𝑐 if ∠𝐶 = 30°.
B
A C
18
b
c
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Right Triangles and Trigonometry
Find the value of the six trigonometric functions for ∠𝐺
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Trig Functions for Any Angle
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Trigonometry of Complements
Find a cofunction with the same value as the following expressions:
cos 20° cot 40°
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Signs of Trigonometric Functions
ALL STUDENTS
TAKE CALCULUS
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Signs of Trigonometric Functions
Name the quadrant in which 𝜃 lies if:
(a) tan 𝜃 is positive and sin 𝜃 is negative
(b) csc 𝜃 is positive and cos 𝜃 is positive
(c) sec 𝜃 is negative and cot 𝜃 is negative
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Reference Angles
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Using Reference Angles
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Using Reference Angles
Use reference angles to find the exact values for each of the following functions:
(a) sin 4𝜋
3
(b) cos 7𝜋
6
(c) tan −120°
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Using Reference Angles
Use reference angles to find the exact values for each of the following functions:
(a) sec 7𝜋
3
(b) csc 13𝜋
6
(c) cot 405°
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Exit Ticket/Homework
PART 1:
The distance 𝑎 across the pond is unknown. To find this distance, a surveyor took the measurements shown. Find 𝑎.
1200 yards
PART 2:
For each angle below, find a reference angle 𝜃′ and use it to give the values of the six trig functions.
(a) 𝜃1 =15𝜋
6 (b) 𝜃2 = −
5𝜋
4 (c) 𝜃3 = 420°
HOMEWORK: (due Jan 19) Pg. 513, #4-80 (mult. of 4)